A note on Le Barz's formulas (Q1864687)

In this article the author studies smooth projective surfaces in 4-space with no 5-secant lines. She gives a list of such surfaces of degree less than or equal to 11 and with at most a finite number of lines. Furthermore, she shows that a surface in 4-space with infinitely many lines and no proper 5-secant lines must be a rational cubic scroll or an elliptic quintic scroll. Le Barz enumerative formulas for \(n\)-secants are the main tools used: see \textit{P. Le Barz}, Enseign. Math., II. Sér. 33, 1-66 (1987; Zbl 0629.14037), C. R. Acad. Sci., Paris, Sér. I 292, 797-800 (1981; Zbl 0492.14045) and Enumerative geometry, Proc. Conf., Sitges 1987, Lect. Notes Math. 1436, 151-188 (1987; Zbl 0721.14028).